A poultry farmer that dabbles in statistics is interested in exploring the relationship between two types of feed (layer pellets and scratch), water, and the output of his laying hens. For ten days he records the number of ounces of layer pellets and scratch the hens consume and the number of fluid ounces of water and tracks the number of eggs that are produced. After running a multiple regression model, he obtains the following report. What is the best interpretation of these statistics? Regression Statistics
$$\begin{array} { | l | c | }
\hline \text { Multiple R } & 0.993633 \
\hline \text { R Square } & 0.987307 \
\hline \text { Adjusted R Square } & 0.98096 \
\hline \text { Standard Error } & 0.213764 \
\hline \text { Observations } & 10 \
\hline
\end{array}$$
A)The probability that the number of eggs is correctly predicted by the amount of scratch, layer pellets, and water consumed is 99.36%.
B)The prediction of the amount of eggs is 98.7% accurate based on the amount of scratch, layer pellets, and water consumed.
C)98.7% of the variability in egg production is explained by the amount of water, scratch, and layer pellets consumed.
D)The prediction of the amount of eggs is 99.36% accurate based on the amount of scratch, layer pellets, and water consumed.

Question

A poultry farmer that dabbles in statistics is interested in exploring the relationship between two types of feed (layer pellets and scratch), water, and the output of his laying hens. For ten days he records the number of ounces of layer pellets and scratch the hens consume and the number of fluid ounces of water and tracks the number of eggs that are produced. After running a multiple regression model, he obtains the following report. What is the best interpretation of these statistics? Regression Statistics
$$\begin{array} { | l | c | } 
\hline \text { Multiple R } & 0.993633 \
\hline \text { R Square } & 0.987307 \
\hline \text { Adjusted R Square } & 0.98096 \
\hline \text { Standard Error } & 0.213764 \
\hline \text { Observations } & 10 \
\hline
\end{array}$$
A)The probability that the number of eggs is correctly predicted by the amount of scratch, layer pellets, and water consumed is 99.36%.
B)The prediction of the amount of eggs is 98.7% accurate based on the amount of scratch, layer pellets, and water consumed.
C)98.7% of the variability in egg production is explained by the amount of water, scratch, and layer pellets consumed.
D)The prediction of the amount of eggs is 99.36% accurate based on the amount of scratch, layer pellets, and water consumed.

Quizplus · Accepted Answer

The R Square value of 0.987307 indicates that 98.7% of the variability in egg production can be explained by the amount of water, scratch, and layer pellets consumed. This means that these three variables are highly predictive of the number of eggs produced. The other statistics, such as Multiple R and Standard Error, provide additional information about the strength and reliability of the relationship. However, neither A nor B accurately reflect the meaning of these statistics, and D is not quite correct as it refers to prediction accuracy rather than explaining variability.

A Poultry Farmer That Dabbles in Statistics Is Interested in Exploring